需求信息非对称情况下零售商最优订货问题研究

考虑需求信息非对称环境下多个存在竞争的零售商的最优订货问题,每个零售商的需求分布函数未知,传统的通过最大化期望利润来求解最优订货量的方法此时不再适用,转而应用稳健优化中使用的方法-最小化最大后悔值方法.首先给出了零售商最优订货量的一般形式.其次考虑了问题的两种特殊情形:对称博弈、两个零售商的最优订货模型,得到:对称博弈存在Nash平衡点、竞争使得零售商订货量增大、信息不对称使得零售商订货量降低并且零售商的最优订货量在一定条件下会随回收残值的增大而增大;两个零售商最优订货模型下的最优订货量的具体形式.     

多个过度自信零售商最优订货策略研究

研究在竞争环境下过度自信零售商对市场需求的信念存在偏差时的订货决策问题.在仅知市场需求的均值和支集的情况下,应用最大绝对后悔最小化准则,建立多个过度自信零售商的鲁棒订货模型.证明了具有多个零售商竞争的报童博弈的鲁棒优化Nash均衡解的存在性,并导出了最优决策的封闭表达式.讨论过度自信行为对零售商最优订货量和期望利润的影响.数值分析结果表明:在最小化最大绝对后悔值准则下,过度自信零售商获得的实际期望利润要低于其获得的信念期望利润;在两个零售商的非对称博弈情形,过度自信零售商获得的实际期望利润要高于完全理性零售商获得的期望利润,并且每个零售商获得的实际期望利润还随其竞争对手的过度自信程度的增加而增加.过度自信可以使那些在库存可用性上相互竞争的零售商获益.     

随机中断和随机需求下闭环供应链最优回收定价模型

讨论了由一个制造商、一个零售商和一个第三方回收商组成的闭环供应链的差别定价问题.基于博弈论的理论和方法在集中式和分散式决策情形下分别建立了第三方回收定价模型,并给出了随机中断和随机需求下闭环供应链的最优定价策略组合,最后通过数值例子分析了供应中断对最优批发价和零售价的影响.     

供应中断下最优分配和应急采购策略的比较

最优分配采购策略和应急采购策略被广泛应用于供应中断风险管理中,基于最优分配采购策略和应急采购策略,研究了由两个制造商与两个零售商组成的两级供应链在供应中断下的订购和生产决策问题,给出了最优订购和最优生产策略.通过数值例子就可靠性如何影响制造商的最优价格和利润进行了比较.结果表明:随着可靠性的增加,两个制造商的最优价格呈递减态势,且制造商A的递减幅度小于制造商B的递减幅度;当可靠性低于0.3时,制造商A的最优价格低于制造商B的最优价格,当可靠性高于0.3时,制造商A的最优价格高于制造商B的最优价格.随着可靠性的增加,制造商A的利润呈递减态势,制造商B的利润呈递增态势;当可靠性低于0.8时,制造商A的利润高于制造商B的利润,当可靠性低高于0.8时,制造商A利润低于制造商B的利润.     

需求中断下具零售商激励的双渠道供应链价格与生产决策

研究了由一个制造商和一个零售商所组成的两周期双渠道供应链.在第一周期需求实现之前,建立了生产量;在第二周期,基于第一周期的生产量和需求的实现确定了最优销售价格,进而确定了最优的生产量,实现了生产量的优化.通过需求中断下制造商和零售商的垂直整合,讨论了中断情形下价格和生产量对利润的影响.实证结果证实,集中式供应链的最优价格决策受零售渠道顾客偏好和市场规模变化的影响较为显著.     

需求中断下具有提前期的双渠道供应链的风险规避决策

讨论了由一个制造商和一个零售商所组成的双渠道供应链在需求中断下具有提前期的双渠道供应链的风险规避问题.给出了在需求中断前后的最优价格、最优提前期和最优生产决策.研究表明决策变化量是需求中断量的线性函数,在集中式下最优的决策和销售量与供应链的市场份额和需求中断有关,模型的最优生产体现了一定的稳健性.对于提前期来说,当市场份额较大时,最优提前期关于风险规避系数呈正比例,当市场份额较小时,最优提前期关于风险规避系数呈反比例.     

竞合模式下考虑低碳产品推广补贴的供应链博弈研究

在制造商向零售商提供低碳产品推广补贴的背景下,考虑一个主导制造商和两个跟随零售商构成的供应链,研究两个零售商竞争与合作情况下的供应链减排及低碳产品推广决策,运用Stackelberg博弈理论分别构建了竞争模式、合作模式的模型,得到最优减排水平、低碳产品推广投入及低碳产品推广成本分摊比例.通过比较分析发现:两种模式的最优减排水平不变;与竞争模式相比,合作模式下零售商低碳产品推广投入更低,利润更大,而制造商分摊比例更大,利润更小;当竞争系数大于两个零售商低碳产品推广敏感系数之和时,整个供应链的利润更高,通过谈判协调,可以提高双方的利润.最后运用算例验证了模型的有效性.     

公平偏好下双渠道供应链最优定价策略与协调

在市场需求是一种依赖于销售价格的线性结构下,建立由一个制造商和一个零售商组成的两级双渠道供应链模型.在改进收入共享契约下,分别针对零售商不利不公平厌恶和有利不公平厌恶两种情形,探讨公平偏好对双渠道供应链最优定价策略及契约协调性的影响.研究表明,最优零售价格随零售商不利不公平厌恶偏好增大而减小,随其有利不公平厌恶偏好增大而增大;最优直销价格不受零售商公平偏好影响,制造商始终完全占有直销渠道的销售收入;最优批发价格大小与零售商收入共享比例和公平偏好程度有关;改进收入共享契约仅在零售商不利不公平厌恶偏好下能够实现双渠道供应链协调.     

制造商质量投入竞争与合作的双渠道供应链动态博弈研究

针对具有不同质量投入和服务投入的双渠道供应链,主要研究其成员最优均衡决策问题.构建了包含两个制造商和一个零售商的两级双渠道供应链决策模型;采用微分博弈确定在制造商竞争和合作两种模型下各成员的最优均衡决策及其利润,并着重探讨质量投入系数、服务竞争系数和传统渠道市场占有率这三个关键参数对它们的影响;用算例对该模型进行仿真分析研究结果表明:在竞争模型下零售商的利润随着传统渠道市场占有率、质量投入竞争和服务竞争的增大而增大,但合作模型下的利润与服务竞争无关;制造商合作时制造商的利润之和提高,且两个制造商在两个渠道边际利润和之比在一定范围内,两个制造商会有合作意愿,但零售商的利润下降.研究能够为各成员企业的最优均衡决策提供支持和参考.     

基于最优让步均衡协调策略的供应链差价补偿机制研究

制造商为了激励零售商订购更多数量的产品,会在产品零售价下调时提供给零售商一定的补偿,如何制定最优补偿机制是提高供应链收益的关键问题.为此,建立了两阶段销售差价补偿机制下制造商与零售商的博弈模型,分析了纳什均衡解和Stackelberg均衡解下制造商对零售商的差价补偿机制的决策行为,导出了在最优让步均衡策略下差价补偿机制...     

RECENT PROGRESS ON SPHERICAL HARMONIC APPROXIMATION MADE BY BNU RESEARCH GROUP ——In memory of Professor Sun Yongsheng

As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.     

On a class of self-similar processes with stationary increments in higher order Wiener chaoses

We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.     

On a class of Riemann surfaces

It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

CONTENTS OF VOLUME 30

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Instructions for contributions

正Applied Mathematics-A Journal of Chinese Universities,Series B(Appl.Math.J.Chinese Univ.,Ser.B)is a comprehensive applied mathematics journal jointly sponsored by Zhejiang University,China Society for Industrial and Applied Mathematics,and Springer-Verlag.It is a quarterly journal with     

Journal of Mathematical Research with Applications Guide for Authors

正Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics.     

Staircase transportation problems with superadditive rewards and cumulative capacities

A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.To our friend, Philip Wolfe, with admiration and affection, on the occasion of his 65th birthday.Research was supported respectively by the IBM T.J. Watson and IBM Almaden Research Centers and is a minor revision of the IBM Research Report [6].     

Boundedness for commutators of multipliers on Hardy type spaces

In this paper, we study the commutators generalized by multipliers and a BMO function. Under some assumptions, we establish its boundedness properties from certain atomic Hardy space Hb^p（R^n） into the Lebesgue space L^p with p 〈 1.